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  1.  
  2. /* @(#)e_atan2.c 5.1 93/09/24 */
  3. /*
  4.  * ====================================================
  5.  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
  6.  *
  7.  * Developed at SunPro, a Sun Microsystems, Inc. business.
  8.  * Permission to use, copy, modify, and distribute this
  9.  * software is freely granted, provided that this notice
  10.  * is preserved.
  11.  * ====================================================
  12.  *
  13.  */
  14.  
  15. /* __ieee754_atan2(y,x)
  16.  * Method :
  17.  *      1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
  18.  *      2. Reduce x to positive by (if x and y are unexceptional):
  19.  *              ARG (x+iy) = arctan(y/x)           ... if x > 0,
  20.  *              ARG (x+iy) = pi - arctan[y/(-x)]   ... if x < 0,
  21.  *
  22.  * Special cases:
  23.  *
  24.  *      ATAN2((anything), NaN ) is NaN;
  25.  *      ATAN2(NAN , (anything) ) is NaN;
  26.  *      ATAN2(+-0, +(anything but NaN)) is +-0  ;
  27.  *      ATAN2(+-0, -(anything but NaN)) is +-pi ;
  28.  *      ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
  29.  *      ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
  30.  *      ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
  31.  *      ATAN2(+-INF,+INF ) is +-pi/4 ;
  32.  *      ATAN2(+-INF,-INF ) is +-3pi/4;
  33.  *      ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
  34.  *
  35.  * Constants:
  36.  * The hexadecimal values are the intended ones for the following
  37.  * constants. The decimal values may be used, provided that the
  38.  * compiler will convert from decimal to binary accurately enough
  39.  * to produce the hexadecimal values shown.
  40.  */
  41.  
  42. #include "fdlibm.h"
  43.  
  44. #ifndef _DOUBLE_IS_32BITS
  45.  
  46. #ifdef __STDC__
  47. static const double
  48. #else
  49. static double
  50. #endif
  51. tiny  = 1.0e-300,
  52. zero  = 0.0,
  53. pi_o_4  = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
  54. pi_o_2  = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
  55. pi      = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
  56. pi_lo   = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
  57.  
  58. #ifdef __STDC__
  59.         double __ieee754_atan2(double y, double x)
  60. #else
  61.         double __ieee754_atan2(y,x)
  62.         double  y,x;
  63. #endif
  64. {  
  65.         double z;
  66.         __int32_t k,m,hx,hy,ix,iy;
  67.         __uint32_t lx,ly;
  68.  
  69.         EXTRACT_WORDS(hx,lx,x);
  70.         ix = hx&0x7fffffff;
  71.         EXTRACT_WORDS(hy,ly,y);
  72.         iy = hy&0x7fffffff;
  73.         if(((ix|((lx|-lx)>>31))>0x7ff00000)||
  74.            ((iy|((ly|-ly)>>31))>0x7ff00000))    /* x or y is NaN */
  75.            return x+y;
  76.         if((hx-0x3ff00000|lx)==0) return atan(y);   /* x=1.0 */
  77.         m = ((hy>>31)&1)|((hx>>30)&2);  /* 2*sign(x)+sign(y) */
  78.  
  79.     /* when y = 0 */
  80.         if((iy|ly)==0) {
  81.             switch(m) {
  82.                 case 0:
  83.                 case 1: return y;       /* atan(+-0,+anything)=+-0 */
  84.                 case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
  85.                 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
  86.             }
  87.         }
  88.     /* when x = 0 */
  89.         if((ix|lx)==0) return (hy<0)?  -pi_o_2-tiny: pi_o_2+tiny;
  90.            
  91.     /* when x is INF */
  92.         if(ix==0x7ff00000) {
  93.             if(iy==0x7ff00000) {
  94.                 switch(m) {
  95.                     case 0: return  pi_o_4+tiny;/* atan(+INF,+INF) */
  96.                     case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
  97.                     case 2: return  3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
  98.                     case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
  99.                 }
  100.             } else {
  101.                 switch(m) {
  102.                     case 0: return  zero  ;     /* atan(+...,+INF) */
  103.                     case 1: return -zero  ;     /* atan(-...,+INF) */
  104.                     case 2: return  pi+tiny  ;  /* atan(+...,-INF) */
  105.                     case 3: return -pi-tiny  ;  /* atan(-...,-INF) */
  106.                 }
  107.             }
  108.         }
  109.     /* when y is INF */
  110.         if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
  111.  
  112.     /* compute y/x */
  113.         k = (iy-ix)>>20;
  114.         if(k > 60) z=pi_o_2+0.5*pi_lo;  /* |y/x| >  2**60 */
  115.         else if(hx<0&&k<-60) z=0.0;     /* |y|/x < -2**60 */
  116.         else z=atan(fabs(y/x));         /* safe to do y/x */
  117.         switch (m) {
  118.             case 0: return       z  ;   /* atan(+,+) */
  119.             case 1: {
  120.                       __uint32_t zh;
  121.                       GET_HIGH_WORD(zh,z);
  122.                       SET_HIGH_WORD(z,zh ^ 0x80000000);
  123.                     }
  124.                     return       z  ;   /* atan(-,+) */
  125.             case 2: return  pi-(z-pi_lo);/* atan(+,-) */
  126.             default: /* case 3 */
  127.                     return  (z-pi_lo)-pi;/* atan(-,-) */
  128.         }
  129. }
  130.  
  131. #endif /* defined(_DOUBLE_IS_32BITS) */
  132.